On conflicts
Abstract
In this article a mathematical model of conflict situations, based on three binary relations: alliance, conflict and neutrality, is introduced. Axioms for alliance and conflict relations are given and some properties of these relations are investigated.
Further, the strength of an object is introduced. The set of the three relations mentioned above, together with the strength of all objects, is called the situation. Some rules of transformation of situations are introduced and investigated.
Finally, the notion of a capture is defined and the rules of sharing of the capture among objects in a given situation are formulated. Some theorems concerning capture sharing are given.
The approach presented can be used as a starting point for an easy computer simulation of conflict situations.
References (2)
- Z. Pawlak
About conflicts
ICS PAS Reports
(1981) - F. Roberts
Cited by (142)
A three-way conflict analysis model with decision makers’ varying preferences [Formula presented]
2024, Applied Soft ComputingThe preferences of decision makers (DMs) over conflicting states have a significant impact on the stability of the conflict system. However, the DM’s preferences over conflicting states are generally unclear and variable, as they are influenced by the unpredictability of future situations of nature and the psychological behavior of DMs. To deal with multi-issue conflict problems, since the interval grey number and three-way decisions can reveal the mechanism of DMs’ grey and varying preferences in uncertain natural situations, we exploit grey system theory, conflict analysis, and three-way decisions to establish a novel conflict analysis model with varying decision makers’ preferences, and a conflict case of industry-university-research innovation alliance verifies the efficacy and rationality of the model.
Three-way conflict analysis based on hybrid situation tables
2023, Information SciencesThe existing studies about three-way conflict analysis are based on a single type of situation tables. However, due to the complexity and uncertainty of the objective world, the rating types in a situation table may be diverse. We call this kind of situation table as a hybrid situation table. In this paper, we focus on three-way conflict analysis based on hybrid situation tables. First of all, we propose the conception of hybrid situation tables. By aggregating conflict distances for a single type of rating, we give the conception of hybrid conflict distances in a hybrid situation table. On this basis, we establish a three-way conflict analysis model w.r.t. multiple issues based on hybrid situation tables. Secondly, we define (maximal) strong alliances, (maximal) weak alliances, and maximal alliances, which can help to find a conflict resolution method in a hybrid situation table. In order to resolve conflict, we define feasible strategies in a hybrid situation table and use interval-valued decision-theoretic rough sets to approximate maximal strong alliances w.r.t. feasible strategies. Besides, we propose the conception of evaluation functions for finding an optimal strategy. Finally, we explore a governance problem of government to illustrate the validity and feasibility of the proposed method.
Three-way conflict analysis in dual hesitant fuzzy situation tables
2023, International Journal of Approximate ReasoningConflict occurs in all aspects of life, and people tend to consider a variety of factors in the face of it and hesitate to make decisions among multiple choices. This paper performs a three-way conflict analysis in the dual hesitant fuzzy case. Firstly, we propose the concept of dual hesitant fuzzy situation tables (DHFSTs). Subsequently, we trisect the pairs of agents and objectively calculate issue weights by CRITIC method rather than subjective assignments. According to Bayesian minimum risk theory, we derive trisection of agents, in which the state set is calculated objectively. Then, we analyze three issue sets through the conflicting characters of issues, which provides a new way to consider the trisection of issues. In addition, we put forward the definition of maximal coalitions in DHFSTs and give an effective calculation method. Finally, we illustrate the feasibility of the proposed model by analyzing the development plan in Gansu Province, and conduct a brief comparative analysis.
Modeling relationships in three-way conflict analysis with subsethood measures
2023, Knowledge-Based SystemsThe relations on agents and issues are essential topics in three-way conflict analysis. While there is a general agreement on the formulation and understanding of relations regarding individual agents and issues, different opinions have been proposed when it involves agent or issue sets. On the one hand, these opinions provide diverse perspectives on interpreting the relations, enriching approaches to other essential topics in conflict analysis, such as finding a feasible strategy for a group of agents. On the other hand, a general and unified framework still needs to be developed in order to investigate the relations systematically and uniformly. Based on the quantitative subsethood measures, this work presents such a framework and conducts a comprehensive and systematic study of the relations in conflict analysis. We pay particular attention to the agent relations with respect to a set of issues and the relations between individual agents and issue sets, which are in the spotlight of the existing works. For each of them, we present a general formulation of the relations using subsethood measures and show that a few popular existing formulations could be explained and formulated under the presented formulation.
Conflict analysis is one of the most critical application domains whose importance is increasing rapidly nowadays. Attributes involving conflicts frequently occur with opinion, negotiations, and collaborators in decision-making. Taking advantage of the uncertainty present in decision-making, in this paper, we have proposed a system that can solve the problems involving conflicts more adequately.
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A new interval-valued intuitionistic fuzzy rough set (IVIFRS) system is introduced to handle a decision-making problem involving a conflict of interests.
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The proposed system exploits both the notions of rough set and interval-valued intuitionistic fuzzy set theories in sharpening the boundaries of conflicts.
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In the IVIFRS system, the disputes amongst the objectives are measured by the novel conflict distance measure. Further, an interval-valued intuitionistic fuzzy conflict analysis system formulated on the IVIFRS is designed for deciding the conflicting attributes
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Formal concept analysis perspectives on three-way conflict analysis
2023, International Journal of Approximate ReasoningPawlak conflict analysis focuses on three-valued ratings of a set of agents on a set of issues, in which the three values +, 0, and − indicate, respectively, that an agent is positive, neutral, and negative about an issue. According to their shared ratings, we can form different types of agent coalitions and, similarly, different types of issue bundles (i.e., families of issues to be considered together). The main objective of this paper is to introduce and investigate connections of agent coalitions and issue bundles from Wille formal concept analysis perspectives. By interpreting a three-valued rating table as four different formal contexts, we introduce four types of agent coalitions, namely, support, non-opposition, opposition, and non-support coalitions, the corresponding four types of issue bundles, and four lattices of coalition-bundle couplings. The lattices reveal structural information of agents and issues in a conflict situation. To demonstrate the usefulness of the proposed model, we analyze the problem of development planning of the Gansu Province of China.